“Risk Aversion and Expected Utility Theory: A Calibration Theorem,” M. Rabin (2000)

This famous paper expands on Samuelson’s result about repeated lotteries to show that concave utility plus modest risk aversion with modest stakes implies ridiculously large amounts of risk aversion, to the extent that an agent who turns down a lottery paying $11 and $-10 with equal probability must, if he has concave utility and maximizes E(u), turn down some gambles with a large probability of infinite payoff. The point is well-taken, as are the criticisms of misusing expected utility to calibrate laboratory experiments, but the general result doesn’t strike me as particularly worrying for theorists. An axiomatic model is a model, nothing more. Whether in natural science or social science, a model of the world, by definition, is meant to adequately describe some features of the world which we are investigating, nothing more. It is a mistake to interpret a model as a true statement. Expected utility holds – tautologically – given four assumptions about human decisionmaking. To the extent that people make reference-dependent decisions, or have incomplete preferences, or indeed make errors, this is not a refutation of an axiomatic system, but rather a suggestion that, if we believe those features are relevant to the aspect of nature we are studying, then they should be incorporated into the theory used in such an investigation. Expected utility as a framework has only exhausted its life when we find an equally attractive – meaning parsimonious, descriptive, and tractable – model that is strictly more useful – however defined – in all subjects we wish to research.

The bigger worry with Rabin is that the lotteries he investigates as “modest” do not strike me as modest at all. Would that it were true that people turned down lost $100/gain $105 bets because of risk aversion! Note that assumed concavity of utility implies that risk aversion – and not some sort of loss aversion – is what is driving individuals to turn down the bets. Even if no individual were susceptible to such a money pump, I would be glad to walk around Chicago offering to be subjected to the inverse gamble, and I would quickly become rich. To the extent that people state to a researcher that they would turn down such a bet, I don’t see evidence that, given insurance markets and the like, people actually do anything to secure against such small risks. If you accept that line of argument – that in markets people tend to turn down very few positive-value lotteries – and also accept that agents are risk-neutral above a threshhold (say, the $300000 used by Rabin), then the most striking examples in this paper disappear.

http://citeseerx.ist.psu.edu/viewdoc/download?doi= (Final WP)

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